Experimental Status of B-physics

Hitoshi Yamamoto

Univeristy of Hawaii

January 2000, WHEPP-6, Chennai, India

1. B-factories

2. QCD and Weak Interaction

• Inclusive hadronic rates

• Radiative B decays (b→ sγ)

3. CP violation and Unitarity Triangle

• |Vub| and |Vcb| (|Vtd|)

• CP phase β (φ1)

• Direct CP violations

B-factries

< e+e− B-factory accelerators>

Symmetric energies (CESR)

Ee− = Ee+ =MΥ4S

2= 5.29GeV

Asymmetric energies (PEP-II, KEK-B)

e−Ε e+Ε

Υ4S is moving in the lab frame.

ECM = 2√Ee+Ee− = MΥ4S{

EΥ4S = Ee− + Ee+

PΥ4S = Ee− − Ee+

→ βΥ4S =PΥ4S

EΥ4S=

Ee− − Ee+

Ee− + Ee+

CESR (Cornell Electron Strage Ring)

PEP-II (SLAC)

KEK-B (KEK, Japan)

Beam separation

Want collision to occur only at one location

→ Need for beam separation

(avoid parasitic crossings)

CESR: Pretzel orbit

Interweaving e+e− orbits within a single ring

Crossing angle = ±2.3 mrad

PEP-II: Separation by bending magnet

Ee+ 6= Ee−

→ e+, e− beams bend differently

Head-on collision

KEK-B: Finite-angle crossing

Crossing angle = ±11 mrad

Large crossing angle

→Beam instability(synchro-betatron resonance)

Luminosity reduction(geometrical)

machine CESR PEP -II KEK-B

detector CLEO BaBar Belle

circumference (km) 0.768 2.199 3.016

# of rings 1 2 2

Ee+(GeV) 5.3 3.1 3.5

Ee−(GeV) 5.3 9.0 8.0

βΥ4S ∼ 0 0.49 0.39

δE/E 6× 10−4 7× 10−4 7× 10−4

∆tbunch 14ns 4.2ns 2ns

bunch size(w) 500µ 181µ 77µ

” (h) 10µ 5.4µ 1.9µ

” (l) 1.8cm 1.0cm 0.4cm

crossing angle(mrad) ±2.3 0 ±11

Luminosity(cm−2s−1) 1.5× 1033 3× 1033 1034

#BB/s 1.5 3 10

achievements so far

Lum(peak) 8× 1032 1.5× 1033 6× 1032∫Ldt (fb−1) 9.2 1.7 0.3

B-factory Status

• CLEO-3 detector currently running with

a temporary vertex detector.

To be completed in Feb 2000.

• BaBar and Belle currently running.

sin 2β result in summer 2000??

Hadronic machines

• HERA-B: wire target inside e−−p collider at DESY.

HERA-B beging assembled.

To be completed Feb 2000.

• CDF/D0: Fermilab pp collider.

Run2 to begin in fall 2000.

Future machines

• LHCb, BTeV, ATLAS, CMS: ∼2006 and on.

LEP Finished Z0 runs - no more B-physics data.

Some B results still to come on the existing data.

Inclusive Hadronic Rates

Two parameters:

1. Bs.l. ≡ average Br(Hb → Xe−νe)

where Hb =

{B0, B− (Υ4S)

B0, B−, B0s , Nb(any b-baryon) (Z0)

Expect Bs.l.(Υ4S) =τB

τbBs.l.(Z

0)

Bs.l. =1

2.22 + rhad, rhad = rcud + rccs + rno c

(rx : rate in unit of Γs.l.)

2.22 = 1(e) + 1(µ) + 0.22(τ)

2. nc ≡ number of c or c per B decay

Weakly decaying charms: D0, D+, D+s ,Λc,Ξc

Charmonium ≡ 2c if decayed by cc annihilation.

Expect more Λc, Ξc, and Ds on Z0.

nc = 1 +Brccs −Brno c = 1 +rccs − rno c

2.22 + rhad

Theoretical estimates of Bs.l. and nc

Tools

• Local quark-hadron duality

Σ of final states with certain flavor contents

= Σ of the same flavor contents at quark level

Assumed to hold at fixed√s of hadronic system

(‘local’ duality)

• pQCD and Heavy-Quark Expansion (HQE)

Γ(B → f) = Γ0

[a(1 +

λ1

2m2b

+3λ2

2m2b

) + bλ2

m2b

+O(1

m3b

)

](

Γ0 =G2Fm

5b

192π3

)a, b: contains CKM factors, Wilson coefficients (pQCD),

and phase space factors.

λ1,2: ‘non-perturbative’ effects

λ1 = 0 ∼ −0.7 GeV2: time-delation by fermi motion

λ2 = 14(m∗2B −m2

B) = 0.12 GeV2

: chromomagnetic effect

Total effect by λ1,2 ∼ a few % increase.

Not all non-perturbative effects are included in λ1,2.

Effects of various corrections affecting Bs.l. and nc.

(NLO calc by Bagan et. al.)

naive NLO(mc = 0) NLO(mc 6= 0)

rc`ν 2.22 2.22 2.22

rcud 3.0 4.0 4.0

rccs 1.2 1.6 2.1

Bs.l. 0.16 0.13 0.12

nc 1.16 1.17 1.21

Brccs 0.18 0.20 0.25

(rno c ∼ 0.2± 0.1)

Theoretical estimate of Bs.l. strongly depends on the

renormalization scale (also on mc/mb).

(Neubert, Sachrajda)

µ/mb 1 1/2

Bs.l.(%) 12.0± 1.0 10.9± 1.0

nc 1.20± 0.06 1.21± 0.06

(mc/mb = 0.29)

Measurements of Bs.l.

On Υ4S (CLEO) - charge correlation method

• Tag one B by high-P lepton (flavor-tagged)

‘The other side’: select b→ e−, reject b→ c→ e+.

0.15

0.10

0.05

00 1 2 3

pe

(GeV / c)

dB

/ d

p (

0.1

GeV

/ c)

- 1

0970995-001

• Correction for B0-B0 mixing

Correction for b→ c→ e− (B → DDX etc.)

Bs.l. = 10.49± 0.46% (CLEO).

Bs.l. = 10.45± 0.21% (Υ4S, PDG)

Bs.l. on Z0 (LEP)

Experiment Bs.l.(%) method

ALEPH 95 11.01± 0.10± 0.30 1`+ 2`

L3 96 10.68± 0.11± 0.46 e, µ, ν

OPAL 99 10.83± 0.10± 0.20+0.20−0.13 (a)

DELPHI 99 10.65± 0.07± 0.25+0.28−0.12 (b)

(a) b-tag by lifetime.

Fit two neural-net variables to separate

b→ `−, b→ c→ `+, and backgrounds.

(b) 4 methods

1. 1`+ 2`

2. b-tag by lifetime/lepton, Fit p`(B c.m.)

and tag-lepton charge correlation.

3. Use all hadronic events + multi-variate fit

4. Similar to 2. Neural net for flavor id.

Bs.l. = 10.79± 0.17% (Z0 average) .

Measurement of nc

(%) CLEO 96 ALEPH 96 OPAL 96 DELPHI 99

D0 63.6±3.0 60.5±3.6 53.5±4.1 60.05±4.29

D+ 23.5±2.7 23.4±1.6 18.8±2.0 23.01±2.13

D+s 11.8±1.7 18.3±5.0 20.8±3.0 16.65±4.50

Λc 3.9±2.0 11.0±2.1 12.5±2.6 8.90±3.00

Ξ0.+c 2.0±1.0 6.3±2.1 − 4.00±1.60

(cc) 5.4±0.7 3.4±2.4 − 4.00±1.29

nc 1.10±0.05 1.23±0.07 1.17±0.09

• Ξc: ALEPH and DELPHI used the CLEO mea-

surement of Br(B → Ξc) and added Br(Λb → Ξc)

prediction by JETSET.

ALEPH used an old (wrong) CLEO number for

Br(B → Ξc) (nc : 1.23→ 1.21)

• DELPHI values for Ξ0.+c and (cc) + OPAL

→ nc = 1.14± 0.08

Charm counting by vertexing (DELPHI)

Does not depend on charm decay Br’s.

Fit P+H (probability that all tracks with positive lifetime

comes from the primary vertex)

1

10

10 2

10 3

10 4

0 5 10 15 20 25 30 35 40 45

-ln PH+

Num

ber

of e

vent

s

single cdouble cno charmudsc bkg

• 94 data

-4-2024

0 5 10 15 20 25 30 35 40 45

-ln PH+

(dat

a-fit

)/er

ror

Find numbers of 0,1,2-charm decays

nc = 1.147± 0.041± 0.008 (DELPHI)

LEP average:

nc = 1.16± 0.04 (Z0)

Bs.l. vs nc. Theory vs experiments.

1.3

1.2

1.1

1.010 12 14

Bsl(%)

nc

0.25

0.29

0.33

0.25

0.51.0 1.5

m /m

/mb

c b

µ

Ζ

Y(4S)

0

1. Bs.l. for Z0 is converted to Υ4S value (×τB/τb)

2. Discrepancy between theory and Υ4S values is alarm-

ing. Boosting rno c will fix it.

3. Theory and Z0 values are consistent.

Radiative B Decays (b→ sγ)

Triumph of OPE/pQCD

Relevant Hamiltonian for b→ sγ(g):

(use unitarity to factor out VtbV ∗ts)

Heff = −4GF√2VtbV

∗ts

∑i=1,2,7,8

Ci(µ)Oi(µ)

O1 = (cLβγµbLα)(sLαγµbLβ)

O2 = (cLαγµbLα)(sLβγµbLβ)

O7 = emb

16π2 sασµν(1 + γ5)bαFµν

O8 = gsmb

32π2 sασµν(1 + γ5)λaαβbβG

aµν

The lowest level: O7 only.

QCD correction enhances the rate by ∼ 3.

• Complete NLO (order αs) calculation done.

• Scale dependence ∼20% (LO) → ∼5%(NLO).

• ‘Non perturbative effects’ (λ1,2) ∼ +3%.

b→ sγ CLEO (3 fb−1)

Look for an excess of single photon at the B decay

end point (2.1 < Eγ < 2.7 GeV)

Suppress continuum bkg by ‘pseudo B reconstruction’:

γ + 1K0,+ + n+π± + n0π0 (n+ + n0 ≤ 4, n0 ≤ 1) that is

consistent with B

ON Data

Scaled OFF Data

BB- Background

Eγ (GeV)

Wei

ght/(

0.2

GeV

)

(a)

0

50

100

150

200

250

300

350

1.8 2 2.2 2.4 2.6 2.8 3 3.2

Eγ (GeV)

Wei

ght/(

0.2

GeV

)

Background-Subtracted Yield

Spectator Model

(b)

0

10

20

30

40

1.8 2 2.2 2.4 2.6 2.8 3 3.2

Dotted line: shape predicted for mb = 4.88 GeV

and Fermi motion pB = 250 MeV (model dep.)

CLEO

Br(b→ sγ) = (3.15± 0.35

stat

±0.32

sys

±0.26

model

)× 10−4

ALEPH

Br(b→ sγ) = (3.11± 0.80± 0.72)× 10−4

Theory

Br(b→ sγ) = (3.28± 0.33)× 10−4

Agreement is excellent.

’Pseudo B reconstruction’ → b flavor tag.

Mistag rate ∼8% (CLEO)

−0.09 < ACP ≡b− bb+ b

< 0.42

or ACP = (+0.16± 0.14± 0.05)× (1± 0.04)

mistag

Prospect: CLEO has 3× more data

→ soon to produce a result.

Exclusive B → Xs,dγ

(CLEO)

• B+ → K∗+γ, B0 → K∗0γ

K∗+→K+π0,K0π+

K∗0→K+π−,K0π0

B → K∗γ

B → Xsγ, ACP(small in SM) .

• B → K∗2(1430)γ

The same final states as K∗ above.

• B → (ρ/ω)γ

Br(B → (ρ/ω)γ)

B(B → K∗γ)= ξ

∣∣∣∣VtdVts∣∣∣∣2

ξ: SU(3) breaking, phase space, long-distance

<Full reconstruction on Υ4S >

B → f1 · · · fnEnergy and absolute momentum of B known:

EB = Ebeam = 5.290 GeV

|~PB|=√E2

beam −M2B = 0.34 GeV/c

→ require that candidates satisfy

Etot = Ebeam , |~Ptot| = |~PB|

where

Etot ≡n∑i=1

Ei , ~Ptot ≡n∑i=1

~Pi

Instead of Etot and |~Ptot|, we historically use

∆E ≡ Etot − EB (energy difference)

Mbc ≡√E2

beam − ~P 2tot (beam-constrained mass)

B → K∗γ (CLEO)

Br(B0 → K∗0γ) = (4.550+0.715−0.683 ± 0.343)× 10−5

Br(B+ → K∗+γ) = (3.764+0.893−0.831 ± 0.284)× 10−5

B → K∗γ ACP (CLEO)

All modes other than K0π0 are flavor-tagged.

ACP = +0.080± 0.125 (SM ∼ 1%)

B → K∗2(1430)γ (CLEO)

Br(K∗2(1430)(J = 2)→ Kπ) ∼ 50%

K∗(1410)(J = 1) not excluded.

Assuming all K∗2(1430),

Br(B → K∗2(1430)γ) = (1.7± 0.5± 0.1)× 10−5

R ≡ K∗2(1430)γ / K∗(890)γ = 0.4± 0.1

R =

{3.0− 4.9 (Ali,Ohl,Mannel 93)0.4± 0.2 (Veseli, Olsson 96)

B → (ρω)γ (CLEO)

Upper limits (90% c.l. 1996)

Br(B0 → ωγ) < 1× 10−5

Br(B0 → ρ0γ) < 4× 10−5

Br(B− → ρ−γ) < 1× 10−5

→ |Vtd/Vts|2 < 0.45 ∼ 0.56

Updated limit will come soon (3.5 times data).

Unitarity Triangle

Standard-Model quark-W Interaction

Hint(t) =

∫d3x [HqW(x) +H†qW(x)]

HqW(x) =g√2

(u, c, t)L VCKM γµ

d

s

b

L

Wµ

VCKM =

Vud Vus VubVcd Vcs VcbVtd Vts Vtb

(CKM matrix

unitary

)

If one can adjust CP phases of quarks such that

(CP )HqW(x)(CP )† = H†qW(x′) (x′ = (t,−~x))

→ (CP )Hint(t)(CP )† = Hint(t)

S =∑n

(−i)nn!

∫dt1 · · · dtnT (Hint(t1) · · ·Hint(tn))

→ (CP )S(CP )† = S

• Then, the transition amplitude of |i〉 → |f〉 becomes

the same as that of CP |i〉 → CP |f〉:

〈f |S|i〉 = 〈f |(CP )† (CP )S(CP )†︸ ︷︷ ︸S

(CP )|i〉 = 〈f |(CP )†S(CP )|i〉

I.e., same amp. if particle↔antiparticle and helicity flip

in the initial and final states.

• Or, if |i〉 and |f〉 are eigen states of CP :

CP |i〉 = ηi|i〉 , CP |f〉 = ηf |f〉 ,

Then,

〈f |S|i〉 = η∗fηi〈f |S|i〉 ;

I.e., no transition unless η∗fηi = 1 or ηf = ηi.

CP eigenvalue is conserved.

In general, a 3× 3 unitary matrix has one non-trivial

phase that cannot be rotated away by adjusting the

CP phases of quarks. → CPV.

A Main Question of the CPV Study in B:

‘Is VCKM unitary?’

e.g: orthogonality of d-column and b-column:

VudV∗ub + VcdV

∗cb + VtdV

∗tb = 0

α

βγ

VtdVudVub

* Vtb*

VcdVcb*

α(φ2) ≡ arg

(VtdV

∗tb

−VudV ∗ub

), β(φ1) ≡ arg

(VcdV

∗cb

−VtdV ∗tb

)γ(φ3) ≡ arg

(VudV

∗ub

−VcdV ∗cb

)Note: the definitions of α, β, γ are independent of

quark phases.

For any 3 complex numbers a, b, c, by defintion,

arg(c

−a) + arg(

b

−c) + arg(

a

−b) = π (mod2π)

regardless of a+ b+ c = 0 or not.

It does not test the unitarity.

It tests angles measured are as defined or not.

(e.g. due to penguine contamination etc.)

Need also to measure the lengths of the sides for

unitarity test.

Measurement of |Vcb| (CLEO) (1999)

B → D0,+`ν

dΓ

dw=G2F |Vcb|2FD(w)2

48π3(mB +mD)2m3

D(w2 − 1)3/2

w: γ-factor of D in B frame.

FD(1) = 1 in the HQ limit.

3070299-001

500

400

300

200

100

00.05

0.04

0.03

0.02

0.01

01.0 1.3 1.6

( b )

( a )

~

Eve

nts

/ 0.0

6

w

IIII

FD

(w)

Vcb

Br(B0 → D+`ν) = 2.09± 0.13± 0.18%Br(B− → D0`ν) = 2.21± 0.13± 0.19%

|Vcb|FD(1) = 0.0416± 0.0047± 0.0037|Vcb| = 0.042± 0.005± 0.004± 0.004

(FD(1)=1.0±0.1)

B → D∗0,+`ν (CLEO) (1995)

dΓ

dw=G2F |Vcb|2F (w)2

48π3(mB +mD∗)

2m∗3D

×√w2 − 1

[4w(w + 1)

1− 2wr + r2

(1− w)2+ (w + 1)2

]r = mD∗/mB

F (1) = 1 in the HQ limit.

Y1.00 1.10 1.20 1.30 1.40 1.50

3330994-01640

20

0

20

0

( a ) Linear Fit

( b ) Quadratic Fit

x F

( y

) x

10

||

V cb

3

|Vcb|F (1) = 0.0351± 0.0019± 0.0018|Vcb| = 0.0383± 0.0021± 0.0020± 0.0011

New preliminary Br’s:

Br(B0 → D∗+`ν) = 4.91± 0.17± 0.42%Br(B− → D∗0`ν) = 5.13± 0.54± 0.64%

New DELPHI result ON B → D∗+`ν (1999)

Br(B0 → D∗+`ν) = 5.22± 0.12± 0.55%

|Vcb|A(1) = 0.0380± 0.0013± 0.0016|Vcb| = 0.0417± 0.0015± 0.0017± 0.0014

(A1(1)∼F (1)=0.91±0.03)

LEP combined result on |Vcb|:

Inclusive (40.8± 0.4± 2.0)× 10−3

Exclusive (38.4± 2.5± 2.2)× 10−3

average (40.2± 1.9)× 10−3

• The agreement between exclusive and inclusive in-

dicates validity of global quark-hadron duality.

• D∗`ν has more yield near w = 1 than D`ν

→ less model dependence.

Inclusive b→ u`ν measurements at LEP

ALEPH, DELPHI, L3 combined

Br(b→ u`ν) = (1.67± 0.35± 0.38± 0.20

model

)× 10−3

|Vub| =(

4.05+0.39−0.46

+0.43−0.51

+0.23−0.27 ± 0.02

τB

±0.16

Theory

)× 10−3

10 3

10 4

0 0.2 0.4 0.6 0.8 1

b → u l νb → c l νb → c → lotherev

ents

/ 0.

1

a)

NNbu

ALEPH

0

500

1000

1500

2000

2500

0 0.2 0.4 0.6 0.8 1

b)

NNbu

-100

0

100

200

0 0.2 0.4 0.6 0.8 1

Dat

a -

Mon

te C

arlo

c)

NNbu

-100

0

100

200

0 0.2 0.4 0.6 0.8 1

d)

NNbu

NNbu: neural net variable

(even shape, charged multiplicity, invariant mass etc.)

Exclusive B → ρ−`ν measurements by CLEO

Sensitivity is at high lepton energy

(E` > 2.3 GeV)

Eve

nts

/ (9

0 M

eV/c

2 )

M ( ) (GeV/c2)0.5 1.0 1.5 2.0

3280399-011

40

20

00.5 1.0 1.5 2.0

(b) mode+I 0

20

10

0

(a) mode

Combining with the old results

Br(B → ρ−`ν) = (2.57± 0.29+0.33−0.46 ± 0.41)× 10−4

|Vub| = (3.25± 0.14+0.21−0.29 ± 0.55(th.))× 10−3

(ρ`ν + π`ν)

CLEO B → ρ`ν

3280

399-

015

q2

(GeV

2 /c4 )

All

E

ISG

W2

LC

SR

UK

QC

DW

ise/

Lig

eti+

E79

1B

eyer

/Mel

ikh

ov

(b)

(a)

E

> 2.

3 G

eV

d /dq2 (/10 2 ns 1/ 7 GeV2/c4)

II

05

1015

200

510

1520

4 2

10 5

B-mixing (|Vtd|)

χ ≡ B(t = 0)→ barB(at decay)

B(t = 0)→ all=

1

2

x2

1 + x2

x ≡ ∆m

Γ, (Γ = (1.6ps)−1)

∆md =g4

192π2m2W

|Vtb|2|Vtd|2f2BdB2BdηBf(mt)

• Measure the mixing rate χ → |Vtd|.Large theoretical uncertainties (fBd

and BBd)

• Or, measure Bd mixing and Bs mixing:

∆ms

∆md

=mBs

mBd

∣∣∣∣VtsVtd∣∣∣∣2 ξ2ηBs

ηBd

Less theoretical uncertainty, but

∆ms not measured yet:

∆ms > 14.3 ps−1

A New CLEO Measurement of Bd Mixing

(Preliminary)

On Υ4S:

χ =Both decay as B + Both decay as B

All

• One side: lepton tag

• The other size: partial reconstruction of

B → D∗+nπ ,D∗+ → D0π+

~v(D∗) ∼ ~v(π+) allows the reconstruction of B →D∗+nπ without D0.

mixed unmixed

e-tag 210± 17 838± 30

µ-tag 191± 16 626± 26

Correct for mistags

χd = 19.7± 1.3%